1. Field of the Invention
The present invention relates to interferometry. More particularly, the present invention relates to methods and apparatus for imaging wavefronts. The methods and apparatus of the present invention may be implemented in measuring systems that measure various parameters of test objects by simultaneously generating a plurality of phase-shifted interferograms.
2. Description of the Related Art
Phase-shift interferometry is an established method for measuring a variety of physical parameters ranging from the density of gasses to the displacement of solid objects. Interferometric wavefront sensors can employ phase-shift interferometers to measure the spatial distribution of relative phase across an area and, thus, to measure a physical parameter across a two-dimensional region. An interferometric wavefront sensor employing phase-shift interferometry typically consists of a spatially coherent light source that is split into two wavefronts, a reference wavefront and an object wavefront, which are later recombined after traveling different optical paths of different lengths. The relative phase difference between the two wavefronts is manifested as a two-dimensional intensity pattern known as an interferogram. Phase-shift interferometers typically have an element in the path of the reference wavefront which introduces three or more known phase steps or shifts. By detecting the intensity pattern with a detector at each of the phase shifts, the phase distribution of the object wavefront can be quantitatively calculated independent of any attenuation in either of the reference or object wavefronts. Both continuous phase gradients and discontinuous phase gradients (speckle waves) can be measured using this technique.
Temporal phase shifting using methods such as piezo-electric driven mirrors have been widely used to obtain high-quality measurements under otherwise static conditions. The measurement of transient or high-speed events requires either ultra high-speed temporal phase shifting (i.e., much faster than the event timescales), which is limited due to detector speed, or spatial phase shifting that can acquire essentially instantaneous measurements.
Several methods of spatial phase shifting have been disclosed in the prior art. In 1983 Smythe and Moore described a spatial phase-shifting method in which a series of conventional beam splitters and polarization optics are used to produce three or four phase-shifted images onto as many cameras for simultaneous detection. A number of United States patents, such as U.S. Pat. Nos. 4,575,248; 5,589,938; 5,663,793; 5,777,741; and 5,883,717, disclose variations of the Smythe and Moore method where multiple cameras are used to detect multiple interferograms. One of the disadvantages of these methods is that multiple cameras are required and complicated optical arrangements are need to produce the phase-shifted images, resulting in expensive complex systems.
Other methods of spatial phase shifting include the use of gratings to introduce a relative phase step between the incident and diffracted beams, an example of which is disclosed in U.S. Pat. No. 4,624,569. However, one of the disadvantages of these grating methods is that careful adjustment of the position of the grating is required to control the phase step between the beams.
Spatial phase shifting has also been accomplished by using a tilted reference wave to induce a spatial carrier frequency to the pattern, an example of which is disclosed in U.S. Pat. No. 5,155,363. This method requires the phase of the object field to vary slowly with respect to the detector pixels; therefore, using this method with speckle fields requires high magnification.
Yet another method for measuring the relative phase between two beams is disclosed in U.S. Pat. No. 5,392,116, in which a linear grating and four detector elements are used. This method has a number of drawbacks, including the inability to measure of wavefronts (i.e., the spatial phase distribution across the profile of a beam) and to form contiguous images on a single pixilated detector such as a standard charge coupled device (CCD).
Finally, it is noted that wavefront sensing can be accomplished by non-interferometric means, such as with Shack-Hartmann sensors which measure the spatially dependent angle of propagation across a wavefront. These types of sensors are disadvantageous in that they typically have much less sensitivity and spatial resolution than interferometric wavefront sensors and are not capable of performing relative phase measurements such as two-wavelength interferometry.
It is one object of the present invention to provide an interferometric wavefront sensor that incorporates spatial phase shifting but avoids the complexity of multi-camera systems by using a single two-dimensional pixilated detector, such as a standard charge coupled device (CCD) camera.
It is another object of the present invention to provide methods and apparatus for performing two-wavelength interferometry that utilize a compact spatial phase-shifting device to acquire data at high speeds and provide improved tolerance to vibration.
It is yet another object of the invention to provide methods and apparatus for dividing an incoming wavefront into four sub-wavefronts that are imaged substantially contiguous to maximize the coverage of a pixilated area detector, while minimizing the number of necessary optical components to provide a compact system.
It is still another object of the invention to provide methods and apparatus for introducing a phase shift between orthogonally polarized reference and object wavefronts that is uniform across each sub-wavefront and not sensitive to the positioning of a diffractive optical element.
According to one aspect of the invention, apparatus for splitting a wavefront and producing four substantially contiguous images of the wavefront consists of an input plane, a first lens element, a diffractive optical element, a second lens element, and an output plane. The lens elements are placed in a telescopic arrangement (separated by the sum of their focal lengths) and the diffractive optical element is placed at or near the mutual focal points. The diffractive optical element produces four output wavefronts (or beams) from a single input wavefront. In a preferred embodiment the diffractive element produces four diffracted orders of equal intensity and symmetric to the incident axis so that it can be characterized by a single divergence angle xcex1 and a radial angular spacing of xcex2. The diffractive optic is constructed to suppress the zero order component to the greatest extent possible. Alternatively, the diffractive optical element may produce three diffracted orders each of equal intensity with the transmitted zero order beam. The diffractive optic may include a wedged substrate to provide a uniform angular tilt to all four beams so they propagate symmetrically to the axis of the incident beam. Again, the compound diffractive optical element is characterized by a single divergence angle xcex1 and a radial angular spacing xcex2. Any higher-order diffracted components from the diffractive optic should be at least twice the angular divergence. The focal length of the second lens may be selected to be equal to the detector size divided by two times the tangent of the diffractive optic""s divergence angle. The front lens may be chosen to produce an overall system magnification equivalent to the original wavefront dimension divided by half the detector size.
According to another aspect of the invention, apparatus for introducing a uniform phase-shift between orthogonally polarized reference and object wavefronts includes a polarization mask element made of discrete sections. Each section includes a phase retardation plate or a blank and a linear polarizer. The relative angular orientation of the phase retardation plate and linear polarizer is selected to be different for each discrete section. In one exemplary embodiment, the mask element includes four quadrants each providing a phase shift of xcfx80/2 relative to the clockwise adjacent quadrant.
According to still another aspect of the present invention, a system for providing an improved wavefront sensor includes a wavefront splitting element, a polarization mask element, a pixilated detector element, a polarization interferometer, and a computer. The phase of an object beam can be measured with a single frame of data acquired from the pixilated detector.
Yet another aspect of the invention provides a two-wavelength interferometer including a wavefront sensor with a tunable laser or multiple laser sources. Multiple wavefronts are measured at each of several wavelengths with the relative phase values subtracted to determine the contour of an object.
Other objects, features, and advantages of the present invention will become apparent to those skilled in the art from a consideration of the following detailed description taken in conjunction with the accompanying drawings.